The integer a such that a ≡ 43 (mod 23) and −22 ≤ a ≤ 0 is -3. A zero, a positive natural number, or a negative integer with a minus sign is an integer.
What do we mean when we say that integers are congruent to modulo?When two positive integers a and b are divided by a positive integer n, they are said to be congruent modulo n (or an is congruent to b modulo n), or if a b is divisible by n. It can be expressed as a b mod n, where n is the modulus.If n is a positive integer, then the integers a and b are said to be congruent modulo n, as denoted by the expression a b (modn).Division algorithm Allow dd and aa to be both positive integers. Following that, there are two distinct integers, qq and rr, where rd0 and rd are equal, resulting in a = dq + ra = dq + rTherefore,
-3 is in between -22 and 0 so a =-3
a ≡ 43 (mod 23) and −22 ≤ a ≤ 0.
a ≡ 43 (mod 23)
≡ 43-22 (mod 23)
Simplifying,
≡ 20 (mod 23)
≡ 20-23 (mod 23)
Then we get,
≡ -3 (mod 23)
-3 is in between -22 and 0 so a =-3
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Using Distributive Property to multiply
28 x 4=
19 x 5=
41 x 6=
List five staple convenience goods that you or your household buys on a regular basis. (you do not need to use complete sentences. 2.5 points)
The five staple convenience goods are:
Food items,
Petrol,
Detergents,
Drinking water, and
Fruits.
Staple convenience goods are those items that are purchased by consumers on a regular basis because they are constantly used by them.
These items are readily available nearby a domestic environment because they are always on a high demand by consumers.
These goods listed above are called staple convenience goods because they share some common features which include:
These goods can be bought in small quantity especially when needed.These goods doesn't require a purchase plan before they are bought.They are bought frequently and regularly.Learn more here:
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a state park charges a $6 entry fee plus $7.50 per night of camping write an algebraic expression for the cost in dollars of entering the park and camping for n nights
When an opinion poll calls landline telephone numbers at random, approximately 30% of the numbers are working residential phone numbers. the remainder are either non-residential, non-working, or computer/fax numbers. you watch the random dialing machine make calls. x is the number of calls until the first working residential number is reached. does x have a binomial distribution? give your reasons?
The probability that the factory manufactures a defective light bulb is 0.02. find the probability that the plant manufactures 100 non defective light bulbs before it manufactures 10 defective ones
A model is made of a car. The car is 10 feet long and the model is 7 inches long. What is the ratio of the length of the car to the length of the model? A. 10 : 7 B. 7 : 120 C. 120 : 7 D. 7 : 10
Final answer:
To find the ratio of the car's length to the model's length, first convert the car's length to inches (120 inches), then compare it to the model's length (7 inches), which gives a ratio of 120 : 7.
Explanation:
The question asks for the ratio of the length of the car to the length of the model. First, it's essential to convert both measurements to the same unit for an accurate comparison. The car is 10 feet long, and since 1 foot equals 12 inches, the car's length in inches is 10 feet × 12 inches/foot = 120 inches. The model is 7 inches long. Therefore, the ratio of the length of the car to the length of the model is 120 inches to 7 inches, which simplifies to 120 : 7.
if you deposit $4000 into an account paying 9% annual interest compounded monthly, how long until there is $10000 in the account?
To determine how long it will take for $4000 to grow to $10000 with an interest rate of 9% compounded monthly, we can use the formula for compound interest and solve for t. The time t is approximately 7.17 years.
Explanation:To find out how long it will take for $4000 to grow to $10000 at an interest rate of 9% compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = total amount after time t
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
By plugging in the given values, we can solve for t:
$10000 = $4000(1 + 0.09/12)^(12t)
Dividing both sides by $4000, we get:
2.5 = (1 + 0.0075)^(12t)
Taking the natural logarithm of both sides, we have:
ln(2.5) = ln(1.0075)^(12t)
Using logarithmic properties, we can isolate t:
12t = ln(2.5) / ln(1.0075)
t = ln(2.5) / (12 * ln(1.0075))
Calculating the value of t, we find that it will take approximately 7.17 years for the account to reach $10000.
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What does x equal in 3(x+3)-2<25
The graph above can be extrapolated to determine:
Boyle's Law
PV = k
absolute zero
VT = k
nothing
We can see that
when it is extrapolated
The curve is going downward
and it is till it touches temperature axis
so, we can find point there
It intersects at temperature =-280C
Since, it is x-intercept
so, y will be 0 at that point
so, Volume will be 0 when temperature is -280C
and this is absolute zero definition of volume function
so, Absolute zero.........Answer
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
she gets 145 every week, but paid every other week
so 145 *2 = 290
her pay check will increase by $290
A line has slope 2/3 and y–intercept −2.
Which answer is the equation of the line?
(picture is my choices)
The generic form of straight line consisting of slope and y intercept is given by
y = mx + c
Where 'm' is the slope of the straight line and 'c' is the y-intercept
In the problem, it is given that slope of the line is 2/3 and y intercept is -2 :
m = ²/₃
c = -2
By putting these values in the equation above, we get:
y = ²/₃x - 2
Hence, the second option is correct.
Hope it helps ..!!
Thank you :)
The author purchased a slot machine configured so that there is a 1/2000 probability of winning the jackpot on any individual trial. Although no one would seriously consider tricking the author, suppose that a guest claims that she played the slot machine 5 times and hit the jackpot twice. Find the probability of at least 2 jackpots in 5 trials. Find the probability of exactly 2 jackpots in 5 trials
How to determine the function is even odd or neither
f(x)=5-3x
if the function is mirrored about the y axis, it is even
use -x in place of x and compare the equations
lets use 2 for x
so given formula would be 5-3(2) = 5-6 = -1
replace x with -x you would have 5-3(-2) =5-(-6) = 5+6 =11
since -1 does not = 11 the function is neither
even =f(x), odd = -f(x), neither f(x) doesn't equal -f(x)
example of odd:
f(x) = x^5 +x, replace x with -x
f(-x) = (-x)^5 +-x
=-x^5-x
=-(x^5+x)
=-f(x)
ODD
Example of even:
f(x) = 1-x^4
f(-x) = 1-(-x)^4
=1-x^4
=f(x)
EVEN
Example of Neither:
f(x) = 2x-x^2
f(-x) = 2(-x)-(-x)^2
=-(2x+x^2)
does not equal f(x)
NEITHER
A cyclist rides his bike at a rate of 18 miles per hour. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 5 hours In your computations, assume that 1 mile is equal to 1.6 kilometers. do not round your answers
A dog weighs 2 pounds more than a cat. 3 cats and 4 dogs together weigh 43 pounds. How much does a dog weigh? How much does a cat weigh?
Write each percentage as a mixed number and write in simplest form
Answer:
[tex]\large\boxed{551.5\%=5\dfrac{103}{200}}[/tex]
[tex]\large\boxed{0.5\%=\dfrac{1}{200}}[/tex]
[tex]\large\boxed{350\%=3\dfrac{1}{2}}[/tex]
Step-by-step explanation:
[tex]p\%=\dfrac{p}{100}\\\\27)\ 551.5\%=\dfrac{551.5}{100}=\dfrac{551.5\cdot10}{100\cdot10}=\dfrac{5515}{1000}=\dfrac{5515:5}{1000:5}=\dfrac{1103}{200}=5\dfrac{103}{200}\\\\29)\ 0.5\%=\dfrac{0.5}{100}=\dfrac{0.5\cdot10}{100\cdot10}=\dfrac{5}{1000}=\dfrac{5:5}{1000:5}=\dfrac{1}{200}\\\\31)\ 350\%=\dfrac{350}{100}=\dfrac{35}{10}=\dfrac{35:5}{10:5}=\dfrac{7}{2}=3\dfrac{1}{2}[/tex]
What is the sign of the product (8)(−23)(−21)(−29)? (5 points)
Positive, because the products (8)(−23) and (−21)(−29) are negative, and the product of two negative numbers is positive
Positive, because the products (8)(−23) and (−21)(−29) are positive, and the product of two positive numbers is positive
Negative, because the product (8)(−23) is positive and the product (−21)(−29) is negative, and the product of a positive number and a negative number is negative
Negative, because the product (8)(−23) is negative and the product (−21)( −29) is positive, and the product of a negative number and a positive number is a negative number
-11-X=-18 What is X? hel-pppppp
The measures of a sphere with a volume of 972pi in^3 are multiplied by 1/3.
What is the volume of the sphere?
A) 324pi in^3
B) 108pi in^3
C) 54pi in^3
D 36pi in^3
What is the solution of the system of equations shown in the graph ?
a. (0, 2) c. (0, 4)
b. (2, 0) d. (0, -1)
The solution of graphed equations is the point of intersection of the equations.
The ordered pair that represent the solution is [tex]\mathbf{(b)\ (2, 0)}[/tex]
From the graph, we have the following highlights.
The x-coordinate of the point of intersection is at x = 2The y-coordinate of the point of intersection is at y =0So, the coordinates are 2 and 0
Hence, the ordered pair that represents the solution is [tex]\mathbf{(b)\ (2, 0)}[/tex]
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You have 5 pieces of wood. What is the total length of the wood? 73cm, 1.6m, 2.87m, 325cm and 4.04m
5/6q−1/3q=2/5 Solve for q
A mixture of 17 %disinfectant solution is to be made from 10% and 20% disinfectant solution. How much of each solution should be used if 20 gallons of the 17% solution are needed?
If the sample size is multiplied by 4, what happens to the standard deviation of the distribution of sample means?
Increasing the sample size by a factor of 4 or multiplying it by 4 is equal to increasing the standard error by 1/2. Therefore, the interval will be half as varied. This also works almost for population averages as lengthy as the multiplier from the t-curve doesn't modify much when increasing the sample size.
Write 100 more than 234641
The linear function c = 2 y + 29 models the average cost of a haircut in a certain city, where c, is the average price of a haircut y years after 1995. find the slope for the model. then describe what this means in terms of the rate of change in the average cost of a haircut over time
The rate of change implies that the city's haircut prices are consistently going up over time.
The given linear function is c=2y+29, where c represents the average cost of a haircut y years after 1995.
The slope of the linear function, 2, reflects the rate of change in the average cost of a haircut over time.
This means that for each year after 1995, the average cost of a haircut increases by $2. In other words, the slope indicates that the cost of haircuts is rising at a constant rate of $2 per year. This steady increase implies that the city's haircut prices are consistently going up over time.
The positive slope signifies that the average cost is consistently moving upward as the year progresses. Customers can expect to pay, on average, $2 more for a haircut each year compared to the previous year.
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The slope of the linear function c = 2y + 29 is 2, indicating that the average cost of a haircut increases by 2 units for every 1 increase in the number of years after 1995.
Explanation:The slope of a linear function represents the rate of change. In the given linear function c = 2y + 29, the slope is the coefficient of y, which is 2. This means that for every 1 increase in y (number of years after 1995), the average cost of a haircut will increase by 2 units.
Emilio has 9150 trees to plant in rows on his tree farm. He will plant 125 trees per row. How many full rows of trees will he have?
A bridge club had 22 members with a mean age of 68. Then two new members joined. One was 62 years old, and the other was 80 years old. How did the mean age change after they joined?
The population of Bigville increased from 387,480 to 571,533 in the last 7 years. During the same time period, Smallville increased its population by 53.67%. Which town is growing at the greatest rate and by what factor? (round to nearest hundredth) A) Bigville by a factor of 1.13 B) Bigville by a factor of 6.17 C) Smallville by a factor of 1.13 D) Smallville by a factor of 6.17
Answer:
C!!
Smallville by a factor of 1.13
Bigville --
571,533 - 387,480
387,480
= 47.5%
Smallville -- 53.67
Thus,
53.67
47.5
= 1.129
A container holds 5 gallons of juice. How much is this in pints?
5 gallons is 40 pints.
Hope this helps!